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The Maximum excitation time for a CO2 molecule would be governed by it's spontaneous decay time,That has got to be one of your most ridiculous posts to date.
Not only does the decay time of an excited CO2 molecule have nothing whatsoever to do with the rate at which the bulk air (or ground and ocean) warms, very few of the CO2 atoms actually lose their energy by spontaneous decay. Almost all of them lose the energy in inelastic collisions with neighbouring molecules (at atmospheric temperature and pressure).
I.E. the cycle cannot be longer than that.
The air (neighboring atoms and molecules) increase their energy from the decreases in the CO2 molecule.
The exchange of energy could be conduction(collision), or emission (mostly RF at these energy states).
This is the mechanism by which CO2 causes warming!
It sometimes interrupts the photons heading for space, and sometimes disperses that energy into atmospheric gasses.
I say sometimes, because CO2 cannot absorb the 15 um photons while already excited,
and the re emission energy can be across many wavelengths, some of which do not interact much with the atmosphere.